Finite Group Databasebeta

← #34115237

Subgroups — #34115237

Order 20096.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758259C211yesmaximal, characteristic
2#23758252C211yesmaximal, characteristic
3#23757241C211yesmaximal, characteristic
4D157⋊M16—21no—
5#19097850—21no—
6#19097832C412yescomplemented
7#19097831—21no—
8#19097830C412yes—
9#19097829—21no—
10C2×#14578954C2211yescharacteristic
11C22×#11929434C411yescharacteristic, complemented
12#19097683—21no—
13#19097683—21no—
14C2×M16×C157C411yescharacteristic, complemented
15#14578964—41no—
16#14578963—22no—
17D157⋊C8—41no—
18C4⋊#10597845—41no—
19C22⋊#10597845—22no—
20C4×#10597845—41no—
21#14578954—41no—
22#14578954—41no—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157D411yescharacteristic
26C2×C22⋊D157Q811yescharacteristic
27C2×C4×D157D411yescharacteristic
28C2×C4×D157D411yescharacteristic
29C2×#11929434—21no—
30C2×#11929434—41no—
31C22×C4×C157C2×C411yescharacteristic
32M16×C157—41no—
33C2×C8×C157—21no—
34C2×#10597845—42no—
35#11929441—42no—
36C22×D157C22⋊C411yescharacteristic
37C22×D157C4⋊C411yescharacteristic
38Dic314—41no—
39D628—41no—
40C22⋊D157—41no—
41C22⋊D157—41no—
42C2×Dic157C22⋊C411yescharacteristic
43C2×Dic157C4⋊C411yescharacteristic
44C4×D157—21no—
45C4×D157—21no—
46C4×D157—21no—
47C4×D157—21no—
48#11929434—41no—
49C23×C157C4⋊C411yescharacteristic
50C2×C4×C157—21no—
51C2×C4×C157—21no—
52C2×C4×C157C4211yescharacteristic
53C2×C4×C157C22⋊C411yescharacteristic
54C8×C157—41no—
55C22×C157—21no—
56C22×C157—41no—
57C22×C157#9511yescharacteristic
58C2×D157—21no—
59C2×D157—21no—
60C2×D157—41no—
61C2×D157—41no—
62#10597845—82no—
63C4×C157—21no—
64C4×C157#9911yescharacteristic
65C4×C157#9911yescharacteristic
66Dic157—21no—
67Dic157—21no—
68C2×C157—21no—
69C2×C157—41no—
70C2×C157#34211yescharacteristic
71D157—41no—
72D157—41no—
73C157#139511yescharacteristic, complemented, Sylow
74#1395—1571nomaximal, Sylow
75#413—1571no—
76#410—1571no—
77#408—1571no—
78C2×#41—1571no—
79C2×M16—3141no—
80C2×M16#1059784511yescharacteristic, complemented
81C22×C8—1571no—
82#117—3141no—
83#101—1572no—
84#100—3141no—
85#99—3141no—
86#99—1572no—
87C22⋊C8—3141no—
88C22⋊C8—3141no—
89#41—6281no—
90#41—6281no—
91C2×Q8—1571no—
92C2×D4—1571no—
93C2×D4—1571no—
94C2×D4—1571no—
95C22×C4—1571no—
96C22×C4—1571no—
97C22×C4C2×#1059784511yescharacteristic
98M16—41no—
99M16—3142no—
100M16—6281no—
101C2×C8—21no—
102C2×C8—3141no—
103C2×C8—6281no—
104C2×C8—6281no—
105C4⋊C4—6281no—
106C22⋊C4—3142no—
107C42—6281no—
108C23—1571no—
109C23—1571no—
110C23C4⋊#1059784511yescharacteristic
111Q8—6281no—
112D4—6281no—
113D4—6281no—
114D4—6281no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—3141no—
118C2×C4—3141no—
119C2×C4—3141no—
120C2×C4—3141no—
121C2×C4—6282no—
122C2×C4—1571no—
123C2×C4—1571no—
124C2×C4C4×#1059784511yescharacteristic
125C2×C4C22⋊#1059784511yescharacteristic
126C8—41no—
127C8—6282no—
128C8—6281no—
129C22—21no—
130C22—41no—
131C22—3141no—
132C22—3141no—
133C22—6281no—
134C22—6281no—
135C22(C2×#10597845)⋊C411yescharacteristic
136C4—21no—
137C4—3141no—
138C4—3141no—
139C4—12562no—
140C4#1909782911yescharacteristic
141C4#1909783011yescharacteristic
142C2—21no—
143C2—41no—
144C2—6281no—
145C2—6281no—
146C2#2375815111yescharacteristic
subgroupG/H
centerC4#19097829
commutatorC2×C4×C157C42
FrattiniC22×C4C2×#10597845
FittingC2×M16×C157C4
socleC2×C157#342
prime radical, cosocleC2×#14578954C22
hypercenterC2×M16#10597845
hypocenterC157#1395
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. #19097832C4semidirect
11. C22×#11929434C4semidirect
14. C2×M16×C157C4semidirect
73. C157#1395semidirect
80. C2×M16#10597845semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237582592
#237582522
#237572412
#1395157